Heat kernel estimates for stable-like processes on d-sets

Zhen-Qing Chen and Takashi Kumagai

Stochastic Processes and their Applications, 2003, vol. 108, issue 1, 27-62

Abstract: The notion of d-set arises in the theory of function spaces and in fractal geometry. Geometrically self-similar sets are typical examples of d-sets. In this paper stable-like processes on d-sets are investigated, which include reflected stable processes in Euclidean domains as a special case. More precisely, we establish parabolic Harnack principle and derive sharp two-sided heat kernel estimate for such stable-like processes. Results on the exact Hausdorff dimensions for the range of stable-like processes are also obtained.

Keywords: Besov; spaces; Parabolic; Harnack; inequality; Heat; kernels; Jump; processes; Lévy; systems; Stable-like; processes (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (34)

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